Abstract
In this paper we discuss the uniqueness and existence of solution to a real gas flow network by employing graph theory. A directed graph is an efficient way to represent a gas network. We consider steady state real gas flow network that includes pipelines, compressors, and the connectors. The pipelines and compressors are represented as edges of the graph and the interconnecting points are represented as nodes of the graph representing the network. We show that a unique solution of such a system exists. We use monotonicity property of a mapping to proof uniqueness, and the contraction mapping theorem is used to prove existence.
Highlights
In this paper we investigate the existence and uniqueness of solution to a real gas flow pipeline network by representing the network by graph
The pipelines and compressors are represented as edges of the graph and the interconnecting points are represented as nodes of the graph representing the network
In that paper a gas flow in networks of pipelines is considered. Their models are based on the generalized Riemann problem formulation, where the flow in each connected pipe section is described by the hyperbolic conservation law supplemented by initial conditions within each section of the flow network
Summary
In this paper we investigate the existence and uniqueness of solution to a real gas flow pipeline network by representing the network by graph. In a directed graph representation of a gas network, each edge has been assigned a flow direction. Existence and Uniqueness of Solutions to the Generalized Riemann Problem for Isentropic Flow is discussed in [1]. In that paper a gas flow in networks of pipelines is considered. Their models are based on the generalized Riemann problem formulation, where the flow in each connected pipe section is described by the hyperbolic conservation law supplemented by initial conditions within each section of the flow network.
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